In this paper we present some modified maximum likelihood predictors of the s-th order statistic based on r order statistics of random samples of size n from Rayleigh distribution, where r < s ≤ n. We suggest four types of modifications to the predictive likelihood equations in order to find such predictors. We simulate the values of the bias, mean square prediction error, and likelihood function. On the basis of these criteria, we select the one obtained by the so called Type Il modification to be the best predictor. Its efficiencies compared to those for the best linear unbiased predictors and alternative linear predictors are remarkably high.